For the given problem, determine the equations of the polynomials of degree two whose graphs pass through the given points.

$$(-1,-1),(0,1),(1,-3)$$

Determine the value of $y$ when $x=3.$

Humid air at $75 \mathrm{~psia}$ and $500^{\circ} \mathrm{F}$ and a humidity ratio of $0.018 \mathrm{~lbm} \mathrm{H}_{2} \mathrm{O} / \mathrm{lbm}$ dry air is expanded to $15 \mathrm{~psia}$ in an isentropic nozzle. How much of the initial water vapor has been converted to liquid water at the nozzle outlet?

Suppose that a linear transformation T satisfies

$$T\left(\mathbf{u}_{1}\right)=\left[\begin{array}{l} 2 \\ 1 \end{array}\right], \ T\left(\mathbf{u}_{2}\right)=\left[\begin{array}{r} -3 \\ 2 \end{array}\right]$$

Find $T\left(-2 \mathbf{u}_{1}+3 \mathbf{u}_{2}\right)$

State the first term of each product. a. $(2 x+1)(3 x+4)$ b. $\left(x^{4}+x^{2}\right)\left(3 x^{8}+x^{11}\right)$ c. $x(x+9)$ d. $\left(x^{2}+9\right)(3 x+4)(2 x+6)$ e. $\left(x^{3}+4\right)\left(x^{2}+6\right)(x+5)$

Personal consumption expenditures (in billions of dollars) for several types of recreation from 2012 through 2017 are shown in the table, where $x$ is the expenditures on amusement parks and campgrounds, $y$ is the expenditures on live entertainment (excluding sports), and $z$ is the expenditures on spectator sports.

A model for the data is given by

z = 0.54x - 0.6y + 11.98

Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$.

Do you think one person tan make a difference when it comes to saving earth's resources? Explain.

Calcium sulfate, $\mathrm{CaSO}_4$, is a white, crystalline powder. Gypsum is a mineral, or natural substance, that is a hydrate of calcium sulfate. A 1.000-g sample of gypsum contains $0.791 \mathrm{~g} \mathrm{CaSO}_4$. How many moles of $\mathrm{CaSO}_4$ are there in this sample? Assuming that the rest of the sample is water, how many moles of $\mathrm{H}_2 \mathrm{O}$ are there in the sample? Show that the result is consistent with the formula $\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}$.

Most of the given sentences contain an error in subject-verb agreement. Draw a line through the incorrect verb, and write above it the correct form. If a sentence is already correct, write C above the number.

$\lbrack15\rbrack$ Where's the shirts and pants for the dry cleaners?

Evaluate by using the order of operation: $(2^2+8)\div 4-2$

Solve the problem below using Guess and Check. State your solution in a sentence. Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75 . Find the numbers.

When $25.0 \mathrm{~mL}$ of $0.500 \mathrm{M}$ iron(II) sulfate is combined with $35.0 \mathrm{~mL}$ of $0.332 \mathrm{M}$ barium hydroxide, two different precipitates are formed. (a) Write a net ionic equation for the reaction that takes place. (b) Estimate the mass of the precipitates formed. (c) What are the equilibrium concentrations of the ions in solution?

Express the answers to these operations in scientific notation:
(a) $0.0095+\left(8.5 \times 10^{-3}\right)$
(b) $653 \div\left(5.75 \times 10^{-8}\right)$
(c) $850,000-\left(9.0 \times 10^5\right)$
(d) $\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^6\right)$

Two cars are headed south on the highway at different speeds. Starting when the faster car pulls alongside the slower car, one of the cars accelerates northward for 5.0 s and the other accelerates southward for 5.0 s. At the end of that 5.0-s interval, the two cars have the same speed. Which car is now ahead?

Verify the identity by transforming the lefthand side into the right-hand side.

$$\left(1-\sin ^2 \theta\right)\left(1+\tan ^2 \theta\right) = 1$$